Ann. Phys. Fr.
Volume 19, Number 4, 1994
|Page(s)||433 - 446|
|Published online||01 June 2004|
Theory of quantum nondegenerated liquids
Laboratoire des Champs Magnétiques Intenses, MPI/CNRS, Grenoble
We propose a theory of nondegenerated quantum liquids which is insensitive to the kind of particle statistics and which is applied to condensed helium. We take explicitly into account the fact that the atomic mass and the polarizability are small. We take as the zeroth approximation a system of hard spheres while the attractive forces and the softness of the atom are taken into account as small effects. We show that for temperatures T which are larger than the degeneracy temperature, but less than the temperature at which the atoms are destroyed (ionized), the only characteristic energy scale of the liquid is the energy K0 of its zero point oscillations - the value of the mean kinetic energy of an atom at T = 0. As a result of this fact the "quantum scaling" occurs, i.e., scale invariance of the thermodynamic and kinetic characteristics of the liquid under those changes in T and the density n which leave the reduced temperature T* = T/K unchanged. Through a transformation of the scales of T and n one can determine the thermodynamic functions of any quantum liquid, using the known experimental data of He4. We obtain relations between the thermodynamic characteristics of liquid He 3 and He4.
PACS: 6720 – Quantum effects on the structure and dynamics of nondegenerate fluids
Key words: liquid helium / quantum nondegenerated liquids / kinetic energy / condensed helium / hard spheres / characteristic energy scale / zero point oscillations / quantum scaling / thermodynamic functions / liquid He sup 3 / liquid He sup 4 / He
© EDP Sciences, 1994